Bass, 23, was ordered to stop training earlier this month after failing to make payments on a contract that would have made him the youngest person ever in space.
But he returned to the Star City facility near Moscow on Monday, said Yuri Nikiforov, general director of Atlas Airspace, after officials there decided on Saturday he could resume his preparations.
"He will not go in October for sure, but he just doesn't want to interrupt the programme," said Mr Nikiforov.
The singer is still keen to complete his training so that he can one day fulfil his space travel ambition, added a spokesman for the centre.
"He has shown a great desire to experience the atmosphere of an astronaut's life," the spokesman added.
Bass, who began training at Star City in July, was hoping to join the crew of the next mission to the International Space Station, due to blast off on 28 October.
Cargo container
He had been training with Russian cosmonaut Sergey Zalyotin and Belgian astronaut Frank de Wynne, who will be heading the mission aboard the Soyuz rocket.
However, his plans were disrupted after he failed to come up with the $20m (£12.8m) needed to secure his seat on the voyage.
The Russian Aviation and Space Agency has since said it will send up a cargo container with extra equipment needed on the International Space Station in place of Bass.
Bass had been hoping to follow in the footsteps of the first two space tourists: US businessman Dennis Tito and South African entrepreneur Mark Shuttleworth.
He went as far as undergoing a minor heart operation to rectify an irregular heartbeat in order to be declared fit to fly.
The boy band singer has held the ambition of joining a mission since childhood, when he went to a space camp.
~RS~a~RS~International~RS~q~RS~~RS~z~RS~46~RS~)